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integral inequality; bipartite graph; graph homomorphism; Sidorenko's conjecture

References:

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[4] Conlon, D., Kim, J. H., Lee, C., Lee, J.: **Some advances on Sidorenko's conjecture**. J. London Math. Soc. 98 (2018), 593-608. DOI 10.1112/jlms.12142 | MR 3893193 | Zbl 07000630

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[8] Kim, J. H., Lee, C., Lee, J.: **Two approaches to Sidorenko's conjecture**. Trans. Am. Math. Soc. 368 (2016), 5057-5074. DOI 10.1090/tran/6487 | MR 3456171 | Zbl 1331.05220

[9] Král', D., Martins, T. L., Pach, P. P., Wrochna, M.: **The step Sidorenko property and non-norming edge-transitive graphs**. Available at https://arxiv.org/abs/1802.05007 MR 3873870

[10] Labelle, G., Leroux, P., Ducharme, M. G.: **Graph weights arising from Mayer's theory of cluster integrals**. Sémin. Lothar. Comb. 54 (2005), Article No. B54m, 40 pages. MR 2341745 | Zbl 1188.82007

[11] Li, J. L., Szegedy, B.: **On the logarithmic calculus and Sidorenko's conjecture**. Available at https://arxiv.org/abs/1107.1153

[12] Lovász, L.: **Large Networks and Graph Limits**. Colloquium Publications 60. American Mathematical Society, Providence (2012). DOI 10.1090/coll/060 | MR 3012035 | Zbl 1292.05001

[13] Mayer, J. E., Mayer, M. Göppert: **Statistical Mechanics**. J. Wiley and Sons, New York (1940),\99999JFM99999 66.1175.01. MR 0674819

[14] Royden, H. L.: **Real Analysis**. Macmillan Publishing, New York (1988). MR 1013117 | Zbl 0704.26006

[15] Sidorenko, A. F.: **Inequalities for functionals generated by bipartite graphs**. Discrete Math. Appl. 2 (1991), Article No. 489-504 English. Russian original translation from Diskretn. Mat. 3 1991 50-65. DOI 10.1515/dma.1992.2.5.489 | MR 1138091 | Zbl 0787.05052

[16] Sidorenko, A.: **A correlation inequality for bipartite graphs**. Graphs Comb. 9 (1993), 201-204. DOI 10.1007/BF02988307 | MR 1225933 | Zbl 0777.05096

[17] Szegedy, B.: **An information theoretic approach to Sidorenko's conjecture**. Available at https://arxiv.org/abs/1406.6738